Logic, Proofs and Sets

  1. Let P(x, y) be the proposition x^2 = y, where x and y are in the universe of integers. Determine the truth value of each of the following propositions.
    (a) ∃x P(6, x)
    (b) ∃x P(x, 6)
    (c) ∀x ∃y P(x, y)
    (d) ∃y ∀x P(x, y)

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